Global Strong Solutions of the Vlasov–Poisson–Boltzmann System in Bounded Domains
Global Strong Solutions of the Vlasov–Poisson–Boltzmann System in Bounded Domains
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DOI：
10.1007/s00205-019-01374-9
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发表时间：
2017-10
影响因子：
2.5
通讯作者：
Yunbai Cao;Chanwoo Kim;Donghyung Lee
中科院分区：
文献类型：
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作者：
Yunbai Cao;Chanwoo Kim;Donghyung Lee
当稀带电粒子被限制在一个有界区域内时，边界效应在全局动力学中是至关重要的。我们构造了凸区域上具有扩散边界条件的Vlasov-Poisson-Boltzmann方程组的一个唯一的整体时间解。该构造基于L2-L∞框架，具有某些加权W1，p-空间中分布函数的新型非线性赋范能量估计和自洽电位的C2，δ-估计。此外，我们证明了指数收敛的分布函数的整体麦克斯韦。
When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov–Poisson–Boltzmann system in convex domains with the diffuse boundary condition. The construction is based on anL2-L∞framework with a novelnonlinear-normed energy estimateof a distribution function in some weightedW1,p-spaces andC2,δ-estimates of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellian.